Strong unique continuation for higher order elliptic equations with Gevrey coefficients

Mihaela Ignatova, Igor Kukavica

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We address the strong unique continuation problem for higher order elliptic partial differential equations in 2D with Gevrey coefficients. We provide a quantitative estimate of unique continuation (observability estimate) and prove that the solutions satisfy the strong unique continuation property for ranges of the Gevrey exponent strictly including non-analytic Gevrey classes. As an application, we obtain a new upper bound on the Hausdorff length of the nodal sets of solutions with a polynomial dependence on the coefficients.

Original languageEnglish (US)
Pages (from-to)2983-3000
Number of pages18
JournalJournal of Differential Equations
Volume252
Issue number4
DOIs
StatePublished - Feb 15 2012

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • Carleman estimates
  • Complexity of solutions
  • Gevrey class
  • Strong unique continuation

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